This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A134824 #14 Sep 25 2024 09:46:35 %S A134824 0,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, %T A134824 -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1, %U A134824 -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1 %N A134824 Generated by reverse of Schroeder II o.g.f. %C A134824 The o.g.f. S(x) for A001003 (Schroeder II) satisfies 2*S^2(x) + (1+x)*S(x) + x = 0. %C A134824 Using the Lagrange series for y=S(x) with y=0+x*(y/A(y)) leads to the formula for Schroeder II numbers involving the Narayana triangle A001263. See the Narayana comment by B. Cloitre under A001003 and a multiple differentiation formula given there. %H A134824 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1). %F A134824 G.f.: x*(1-2*x)/(1-x). %F A134824 a(0)=0,a(1)=1, a(n)=-1, n>=2. %Y A134824 If the initial 0 is omitted, we get A153881. %K A134824 sign,easy %O A134824 0,1 %A A134824 _Wolfdieter Lang_, Nov 13 2007